Mean Field Methods for a Special Class of Belief Networks

The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases. The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola and Jordan'...

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Bibliographic Details
Published in:The Journal of artificial intelligence research 2001-01, Vol.15, p.91-114, Article 91
Main Authors: Bhattacharyya, C., Keerthi, S. S.
Format: Article
Language:English
Subjects:
Approximation
Artificial intelligence
Belief networks
Mean field theory
Taylor series
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Summary:The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases. The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola and Jordan' s approach is the first order approximation in Plefka's approach, via a variational derivation. The application of Plefka's theory to belief networks is not computationally tractable. To tackle this problem we propose new approximations based on Taylor series. Small scale experiments show that the proposed schemes are attractive.
ISSN:1076-9757
1943-5037
1076-9757
DOI:10.1613/jair.734